Permutations and Combinations
Distribution of Distinct Objects, Inclusion-Exclusion
jee_adv_2026_mock_p1
Grade 12
Question:
Let the number of ways in which 5 distinct balls can be distributed into 3 distinct boxes such that no box is empty be N. Find the value of N/10.
Step-by-Step Solution
Key Concept: Use inclusion-exclusion principle for distribution of distinct objects.
Step 1: Total ways = 3^5 = 243. Step 2: Ways with at least one empty = 3*2^5 - 3*1^5 = 96 - 3 = 93. Step 3: Ways with no empty = 243 - 93 = 150. N = 150, N/10 = 15.
Correct Answer: 15
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